On the analogy between L-functions and Atiyah-Bott-Lefschetz trace formulas for foliated spaces

Abstract

This paper is motivated by Deninger's programme. First we prove, using Alvarez Lopez-Kordyukov results, an Atiyah-Bott-Lefschetz trace formula for the cohomology groups associated to a ramified leafwise flat line bundle on a riemannian foliation. Then we argue, by precise computations, that cohomology groups associated to ramified leafwise flat vector bundles on a suitable foliated space (whose existence is still unknown) might be useful to study arithmetic L-functions via Atiyah-Bott-Lefschetz trace formulas.

References in corpus (2)

• On a representation of the idele class group related to primes and zeros of L-functions
• Number theory and dynamical systems on foliated spaces

Cited by in corpus (1)

• Analysis on Riemannian foliations of bounded geometry